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Vasseur-Yu [Inventiones mathematicae (2016) and arXiv:1501.06803 (2015)] and by Li-Xin [arXiv:1504.06826 (2015)].More precisely we are able to consider a physical symmetric viscous stress tensor $\\sigma=2\\mu(\\rho)\\,{\\mathbb{D}}(u)+\\bigl(\\lambda(\\rho){\\rm div}u -P(\\rho)\\bigr)\\, {\\rm Id}$ where ${\\mathbb D}(u) = [\\nabla u + \\nabla^T u]/2$ with a shear and bulk 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